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Relevant bibliographies by topics / Cramér-Lundberg Approximation

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Academic literature on the topic 'Cramér-Lundberg Approximation'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Cramér-Lundberg Approximation"

1

Rosenlund, Stig. "Numerical calculation of the Cramér-Lundberg approximation." Scandinavian Actuarial Journal 1989, no. 2 (1989): 119–22. http://dx.doi.org/10.1080/03461238.1989.10413861.

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Minkova, Leda D. "The Pólya-Aeppli process and ruin problems." Journal of Applied Mathematics and Stochastic Analysis 2004, no. 3 (2004): 221–34. http://dx.doi.org/10.1155/s1048953304309032.

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The Pólya-Aeppli process as a generalization of the homogeneous Poisson process is defined. We consider the risk model in which the counting process is the Pólya-Aeppli process. It is called a Pólya-Aeppli risk model. The problem of finding the ruin probability and the Cramér-Lundberg approximation is studied. The Cramér condition and the Lundberg exponent are defined. Finally, the comparison between the Pélya-Aeppli risk model and the corresponding classical risk model is given.

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3

Gyllenberg, Mats, and Dmitrii S. Silvestrov. "Cramér–Lundberg approximation for nonlinearly perturbed risk processes." Insurance: Mathematics and Economics 26, no. 1 (2000): 75–90. http://dx.doi.org/10.1016/s0167-6687(99)00043-8.

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4

Avram, Florin, Andras Horváth, Serge Provost, and Ulyses Solon. "On the Padé and Laguerre–Tricomi–Weeks Moments Based Approximations of the Scale Function W and of the Optimal Dividends Barrier for Spectrally Negative Lévy Risk Processes." Risks 7, no. 4 (2019): 121. http://dx.doi.org/10.3390/risks7040121.

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This paper considers the Brownian perturbed Cramér–Lundberg risk model with a dividends barrier. We study various types of Padé approximations and Laguerre expansions to compute or approximate the scale function that is necessary to optimize the dividends barrier. We experiment also with a heavy-tailed claim distribution for which we apply the so-called “shifted” Padé approximation.

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5

Li, Yan, and Guoxin Liu. "Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model." Discrete Dynamics in Nature and Society 2012 (2012): 1–26. http://dx.doi.org/10.1155/2012/802518.

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We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. The asympt

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6

Schmidli, Hanspeter. "Lundberg inequalities for a Cox model with a piecewise constant intensity." Journal of Applied Probability 33, no. 1 (1996): 196–210. http://dx.doi.org/10.2307/3215277.

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A Cox risk process with a piecewise constant intensity is considered where the sequence (Li) of successive levels of the intensity forms a Markov chain. The duration σi of the level Li is assumed to be only dependent via Li. In the small-claim case a Lundberg inequality is obtained via a martingale approach. It is shown furthermore by a Lundberg bound from below that the resulting adjustment coefficient gives the best possible exponential bound for the ruin probability. In the case where the stationary distribution of Li contains a discrete component, a Cramér–Lundberg approximation can be obt

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7

Schmidli, Hanspeter. "Lundberg inequalities for a Cox model with a piecewise constant intensity." Journal of Applied Probability 33, no. 01 (1996): 196–210. http://dx.doi.org/10.1017/s0021900200103857.

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A Cox risk process with a piecewise constant intensity is considered where the sequence (Li ) of successive levels of the intensity forms a Markov chain. The duration σi of the level Li is assumed to be only dependent via Li . In the small-claim case a Lundberg inequality is obtained via a martingale approach. It is shown furthermore by a Lundberg bound from below that the resulting adjustment coefficient gives the best possible exponential bound for the ruin probability. In the case where the stationary distribution of Li contains a discrete component, a Cramér–Lundberg approximation can be o

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8

Asmussen, Søren, and Tomasz Rolski. "Risk Theory in a Periodic Environment: The Cramér-Lundberg Approximation and Lundberg's Inequality." Mathematics of Operations Research 19, no. 2 (1994): 410–33. http://dx.doi.org/10.1287/moor.19.2.410.

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9

Ekheden, Erland, and Dmitrii Silvestrov. "Coupling and Explicit Rate of Convergence in Cramér–Lundberg Approximation for Reinsurance Risk Processes." Communications in Statistics - Theory and Methods 40, no. 19-20 (2011): 3524–39. http://dx.doi.org/10.1080/03610926.2011.581176.

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10

Miyazawa, Masakiyo. "A MARKOV RENEWAL APPROACH TO THE ASYMPTOTIC DECAY OF THE TAIL PROBABILITIES IN RISK AND QUEUING PROCESSES." Probability in the Engineering and Informational Sciences 16, no. 2 (2002): 139–50. http://dx.doi.org/10.1017/s0269964802162012.

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It is well known that various characteristics in risk and queuing processes can be formulated as Markov renewal functions, which are determined by Markov renewal equations. However, those functions have not been utilized as they are expected. In this article, we show that they are useful for studying asymptotic decay in risk and queuing processes under a Markovian environment. In particular, a matrix version of the Cramér–Lundberg approximation is obtained for the risk process. The corresponding result for the MAP/G/1 queue is presented as well. Emphasis is placed on a straightforward derivati

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Dissertations / Theses on the topic "Cramér-Lundberg Approximation"

1

Yamazato, Makoto. "Non-life Insurance Mathematics." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96535.

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In this work we describe the basic facts of non-life insurance and then explain risk processes. In particular, we will explain in detail the asymptotic behavior of the probability that an insurance product may end up in ruin during its lifetime. As expected, the behavior of such asymptotic probability will be highly dependent on the tail distribution of each claim.<br>En este artículo describimos los conceptos básicos relacionados a seguros que no sean de vida y luego explicamos procesos de riesgo. En particular, tratamos al detalle el comportamiento asintótico de la probabilidad de que un pro

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